Question 2 - 17 marks Katie works for a science museum. She wants to know how long visitors spend at two different exhibits. She measures how long a sample of 20 visitors spend at each exhibit. The results for Exhibits A and B are in Table 1. Table 1 Time spent (in seconds) at two exhibits in a museum Exhibit A Exhibit B 300 25 150 15 180 280 185 10 60 290 50 80 45 310 35 290 80 280 50 180 35 200 80 210 190 170 45 250 25 300 205 20 50 70 170 190 35 220 200(a) (i) Find the summary values for Exhibits A and B, using Dataplotter or otherwise. Copy and complete the table below. Round values, where necessary, to one decimal place. The mean is given for you as a check that you have entered the data correctly. ] Table 2 Summary values for time spent (in seconds) at two exhibits in a museum Exhibit A Exhibit B Min Median Max Mean 199 79 SD IQ range Range (ii) Use the two measures of location to say which exhibit, on average, the visitors spent more time at. Explain your reasoning. [2] (iii) Use all three measures of spread to say which exhibit has the greater variability in the amount of time visitors spent at it. Explain your reasoning. [2](b) (i) Create boxplots for these two datasets (either drawn by hand or as output from Dataplotter or another suitable computer package). Include all the relevant information required for drawing boxplots as set out in Subsection 1.2 of Unit 11. The summary values can be displayed on the borplots themselves or in a table to the side of the chart, as they appear in Dataplotter. [3] (ii) Use the boxplot for Exhibit B to say whether the data are symmetric or skewed. If the data are skewed, then state whether they are skewed to the left or skewed to the right. What does this tell you about the spread of the data for Exhibit B? [2] (iii) Katie tries to summarise what the boxplot for Exhibit A is telling her. Are the following statements true or false? In each case justify your answer. (1) About one-quarter of the people spent more than 160 seconds at Exhibit A. [2] (2) About three-quarters of the people spent more than 205 seconds at Exhibit A. [2](c) Katie also records the number of words spoken by the visitors as they engage with the exhibits. The summary values are in the table below. Table 3 Summary values for the number of words spoken by visitors as they engage with Exhibits A and B Exhibit A Exhibit B Min 2 Median 40 10 Max 62 92 Mean 39.6 18.8 SD 18.8 23.9 1Q range 28 12 Range 60 92 (i) State what kind of data these are: discrete or continuous. Justify your answer. [1] (ii) Katie creates histograms, shown in Figure 1, for the words data, but forgets to label them. Which histogram represents the data for Exhibit A? Explain your answer. [2] 4- frequency 50 100 Number of Words Start Value |0 Interval 10 Use Custom 2 CO frequency N 50 100 Number of Words
